Challenging dyke ascent models using novel laboratory experiments: Implications for reinterpreting evidence of magma ascent and volcanism

Article history: Received 26 July 2017 Received in revised form 21 December 2017 Accepted 2 January 2018 Available online 6 January 2018 Volcanic eruptions are fed by plumbing systems that transport magma from its source to the surface, mostly fed by dykes. Here we present laboratory experiments that model dyke ascent to eruption using a tank filled with a crust analogue (gelatine, which is transparent and elastic) that is injected from below by a magma analogue (dyed water). This novel experimental setup allows, for the first time, the simultaneous measurement of fluid flow, sub-surface and surface deformation during dyke ascent. During injection, a penny-shaped fluid-filled crack is formed, intrudes, and traverses the gelatine slab vertically to then erupt at the surface. Polarised light shows the internal stress evolution as the dyke ascends, and an overhead laser scanner measures the surface elevation change in the lead-up to dyke eruption. Fluorescent passive-tracer particles that are illuminated by a laser sheet are monitored, and the intruding fluid's flow dynamics and gelatine's sub-surface strain evolution is measured using particle image velocimetry and digital image correlation, respectively. We identify 4 previously undescribed stages of dyke ascent. Stage 1, early dyke growth: the initial dyke grows from the source, and two fluid jets circulate as the penny-shaped crack is formed. Stage 2, pseudo-steady dyke growth: characterised by the development of a rapidly uprising, central, single pseudo-steady fluid jet, as the dyke grows equally in length and width, and the fluid down-wells at the dyke margin. Sub-surface host strain is localised at the head region and the tail of the dyke is largely static. Stage 3, pre-eruption unsteady dyke growth: an instability in the fluid flowappears as the central fluid jetmeanders, the dyke tip accelerates towards the surface and the tail thins. Surface deformation is only detected in the immediate lead-up to eruption and is characterised by an overall topographic increase, with axis-symmetric topographic highs developed above the dyke tip. Stage 4 is the onset of eruption, when fluid flow is projected outwards and focused towards the erupting fissure as the dyke closes. A simultaneous and abrupt decrease in sub-surface strain occurs as the fluid pressure is released. Our results provide a comprehensive physical framework upon which to interpret evidence of dyke ascent in nature, and suggest dyke ascent models need to be re-evaluated to account for coupled intrusive and extrusive processes and improve the recognition of monitoring signals that lead to volcanic eruptions in nature.


Introduction
Nearly all volcanic eruptions are fed by magma-filled fractures that propagate through the crust. The dynamics and propagation of magma intrusions has direct influence on the style, longevity and climatic impact of volcanic eruptions by modulating the supply, ascent rate and rheology of magma that reaches the surface (e.g. Caricchi et al., 2014aCaricchi et al., , 2014bIlyinskaya et al., 2017). Magma intrusion precedes volcanic activity (e.g. Patane et al., 2002), can trigger an eruption (e.g. for a review). Dykes are vertical to sub-vertical magma-filled fractures that have high aspect ratio (length/thickness), cut across bedding planes of rock strata, and are the primary conduit to transport magma through the crust to potentially erupt (e.g. Geshi et al., 2010;Gudmundsson, 2006). The rock record provides access to ancient volcanic plumbing systems through field studies of the solidified remnants of magma and deformed surrounding host rock in 2D (e.g. Gudmundsson, 2003) and rarely in 3D (e.g. Kavanagh and Sparks, 2011). However, only a partial record will be preserved and it can be difficult to distinguish pre-, syn-and post-magma intrusion processes. Studying dyke propagation in nature is challenging as only remote measurements can be made during an intrusive event. Evidence of recent dyking has been garnered through geophysical and geodetic measurements of intrusions related to on-land rifting, e.g. Afar and Iceland (Wright et al., 2012). The 2014 dyke intrusion associated with the Bardarbunga volcanic system (e.g. Sigmundsson et al., 2014;Gudmundsson et al., 2014) is arguably the most detailed study of an individual dyking event that led to a fissure eruption. Along with studies of eruptive episodes on Etna, Italy (e.g. González andPalano, 2014, Kahl et al., 2011) and Kilauea, Hawaii (e.g. Cervelli et al., 2002) for example, this has done much to shape and inform our understanding of the geophysical signals of magma intrusion that leads to eruption.
Magma ascends through the crust in regional dykes from deep magma reservoirs primarily due to buoyancy; dyke ascent in nature represents the release of gravitational potential energy on a planetary scale (see Putirka, 2017 for a review) and the release of elastic energy on a regional scale. Magma ascent in dykes is facilitated or impeded by the ability of the magma to flow (its rheology) and deformation of mechanically layered and fractured crustal rocks to accommodate the intrusion. Analogue experimentation and numerical modelling are complementary methods to aid the interpretation of field studies and geophysical surveys of magma intrusion (see Rivalta et al. (2015) and Kavanagh et al. (2017b) for reviews). These dyke propagation models have considered a range of physical processes that impact dyke ascent, including magma buoyancy (e.g. Takada, 1990;Rivalta et al., 2005;Taisne and Jaupart, 2009), solidification (e.g. Taisne and Tait, 2011), deformation of the host material (e.g. Abdelmalak et al., 2012;Kavanagh et al., 2015), interaction with a load or stress field (Watanabe et al., 2002;Daniels and Menand, 2015;Menand et al., 2010;Maccaferri et al., 2014;Pinel and Jaupart, 2000), mechanical layering (e.g. Kavanagh et al., 2006) and pre-existing structures or weak boundaries (e.g. Le Corvec et al., 2013a;Kavanagh et al., 2017a). Technical challenges have meant that analogue experiments have studied either the magma or the host solid, and yet the coupled nature of dyke intrusion means that the simultaneous quantification of both aspects is needed.
In this invited paper, here we describe a new series of novel laboratory experiments where, for the first time, coupled magma flow and host rock deformation is studied during dyke initiation, propagation and eruption. By quantifying flow velocity within the analogue magma with contemporaneous surface deformation and sub-surface strain and stress evolution, we identify previously unrecognised processes that relate the interaction of the intruding magma with its host material to dyke propagation dynamics. We discuss our results in the context of monitoring magma intrusion events and the potential of the rock record to preserve both flow dynamics in crystalline fabrics and evidence of sub-surface deformation during magma intrusion. Our results challenge existing dyke models that are used to interpret surface deformation related to magma intrusion that leads to eruption.

Gelatine preparation, Young's modulus measurement and scaling
To prepare an experiment, forty litres of 2.5 wt% concentration gelatine was made following the guidelines of Kavanagh et al. (2013). To dissolve the mixture, one kilogram of gelatine powder (260 Bloom, 10 mesh, pig-skin gelatine supplied by Gelita UK) was mixed with 19 kg distilled water at approximately 90°C, and this was then diluted further by 20 kg of cold distilled water to create the final desired concentration. Distilled water was used to inhibit bacterial growth and to ensure no impact of local water composition on the gelatine's properties, which has been shown to be susceptible to pH (e.g. Djabourov et al., 1988;Brizzi et al., 2016). In its sol-state (liquid), the hot gelatine mixture was poured into a clear-Perspex square-based tank measuring 40 × 40 × 30 cm 3 (see Fig. 1), any bubbles were then removed from the surface, and the surface was covered in a thin layer of oil to stop dehydration and the development of a tough 'skin'. The experiment tank was then covered in a layer of plastic-wrap and placed into a refrigerator at 5°C to cool and solidify for approximately 20 h (see Table 1).
The Young's modulus of the gelatine solid was measured immediately prior to running an experiment. To do this the experiment tank was taken out of the refrigerator and the plastic wrap and oil layer was removed. A brass cylindrical load (see Table 2) was then placed in centre of the gelatine's surface, and the deflection it caused was measured using a digital micrometer. Following the guidelines from Kavanagh et al. (2013), the diameter of the load was small compared to that of the experiment tank, and the mass was sufficient to cause a measureable deflection (± 0.005 mm). The Young's modulus E was then calculated using the following equation (Kavanagh et al., 2013): where m is the mass of the experiment load, g is gravity, ν is Poisson's ratio of the gelatine (0.5, according to Righetti et al., 2004), D is the load diameter and ω is the deflection it causes to the gelatine's surface. For each experiment, an average of measurements is reported (Table 1) based on two different loads (Table 2) and three measurements per load. Kavanagh et al. (2013) showed that gelatine mixtures in the gelstate (2-5 wt% and 5-10°C) that are injected by water can be appropriately scaled to model dyke propagation in nature. They defined a series of scale factors based on the assumption that the characteristic length scale of the experiment is the buoyancy length L b , which is the length of the fracture when the buoyancy forces balance the resistive forces of the fracture (Taisne and Tait, 2009): where K c is the fracture toughness and Δρ is the density difference between the intruded fluid and the host material. From this follows four scale factors (Kavanagh et al., 2013): Length scale L*: Fig. 1. Schematic sketch of three apparatus setups for imaging dyke experiments where water is injected into the base of a gelatine slab using a peristaltic pump. a) Two polarising sheets (pale grey) are attached to the outside of the tank in the x-z plane. An overhead laser (L1) monitors surface elevation change along a line projected onto the sand-covered gelatine surface (x-y plane), centred on the injection point and perpendicular to the dyke strike-direction. Three HD cameras monitor the growth of the dyke (HD-1 x-z plane, HD-2 y-z plane, and HD-3 x-y plane). b) Particle image velocimetry: a CCD camera (y-z plane) records fluorescing passive-tracer particles within the injected fluid, in a vertical laser sheet projected through the gelatine (centred on the injector, and parallel to the dyke strike-direction). c) Digital image correlation: a CCD camera (x-z plane) records a vertical laser-illuminated sheet through the gelatine (centred on the injector, perpendicular to the dyke strike-direction), which contains suspended passive-tracer particles. Side (i) and plan (ii) views are shown for each method.
Timescale T*: Velocity scale U*: and Stress scale E*: where subscript l is in the laboratory, subscript n is in nature, ρ solid is the density of the host material and ψ is the thickness of the intrusion. In our experiments where water is injected into gelatine: L* = 2 × 10 −3 , and so 1 m in experimental dyke length corresponds with 500 m of dyke length in nature; T* = 9 × 10 −2 , meaning 1 s of the experiment corresponds to 11 s in nature; and U* = 2 × 10 −2 , such that 0.001 m/s in the experiment represents 0.05 m/s in nature. Kavanagh et al. (2013) found that E* = 2 × 10 −6 to 2 × 10 −5 , and as our laboratory measurements of Young's modulus fall within this range and span 2000-3000 Pa (Table 1), this corresponds to rocks in nature that have a Young's modulus of 0.1-1.5 GPa. These values are geologically reasonable and so support the preface that scaled gelatine experiments can be used to describe magma intrusion in nature.

Experimental setup
An experiment is run by injecting water through the base of the solid gelatine slab, using a tapered syringe connected to a peristaltic pump that delivers fluid at a constant volumetric flux (see Table 1). A valve connected to the injection system and a small petroleum jelly seal at the injector tip ensures only water and no air is injected. The orientation of the dyke that is formed is controlled by making a small, vertical cut in the base of the gelatine and inserting the injector into this. It is ensured that the tapered edge of the injector is orientated parallel to the crack. To this basic setup, additional imaging apparatus are used and these are described in more detail in the following sub-sections. These include: gelatine stress field analysis, surface elevation change, dynamics of the intruding fluid flow using particle image velocimetry (PIV), and sub-surface strain analysis via digital image correlation (DIC).

Photoelasticity and surface deformation
Polarising sheets are attached to the outside of the experiment tank, on opposite sides and perpendicular to the dyke strike direction (x-z plane, see Fig. 1a). Gelatine solids are photoelastic, meaning that qualitative stresses and their evolution can be visualised using polarised light. Two light sources illuminate the tank from behind, and two HD video cameras are used to record the sub-surface growth of the experimental intrusions; one is positioned to record the polarised-light view (HD-1, x-z plane), and one images the plane of the dyke in artificial light (HD-2, y-z plane). An additional HD video camera positioned above the experiment tank monitors the free-surface of the gelatine (HD-3, x-y plane). Footage from cameras HD-1 and HD-2 was analysed using the open source software Tracker (Version 4.96) to measure the dyke length, width, and tip position relative to the surface of the gelatine over time.
To monitor the changes in surface topography over time, a Micro-Epsilon laser scanner (L1) is positioned above the analogue setup (Fig. 1a). The laser projects a thin, vertical sheet of light onto the surface of the gelatine; this produces a red line on the gelatine surface that is positioned perpendicular to the dyke strike direction and centred on the injector port. As the gelatine solid is transparent, a thin layer of darkcoloured fine sand (approximate particle size 0.25 mm) is spread evenly over the surface of the gelatine to aid deflection of the laser light. The software ScanCONTROL 5.0 is used to collect data along a 140 mm long transect, with measurement points positioned every 0.5 mm along the projection. Each point along the projection is assigned a height value that corresponds to the distance between the surface of the gelatine and the source of the laser sheet. Changes in the surface topography are recorded at timed intervals of 4 scans per second.
After the experiment, data from the Micro Epsilon laser scanner are exported and manipulated in MATLAB (by Mathworks). Sub-sampling of the dataset produces an elevation profile in 10 s intervals. The cumulative sum of displacement is then calculated across the horizontal transect to illustrate the change in topography over time. Using the statistical analysis software R, a non-parametric fit LOESS curve (Locally Weighted Scatterplot Smoothing) is applied with a span width of 0.3 for the smoothing window.

Particle image velocimetry (PIV) and digital image correlation (DIC)
PIV or DIC are used to quantify fluid flow velocities within the injected fluid or sub-surface strain evolution in the intruded gelatine, respectively. A New Wave Solo-PIV III Laser (L2) provides 50 mJ of energy per pulse at 15 Hz, with a pulse width of 3-5 ns and a wavelength of 532 nm. The laser fires at a repetition rate of 8.875 Hz for the PIV fluid flow experiments (Fig. 1b) and 1 Hz for the DIC gelatine sub-surface deformation experiments (Fig. 1c). The laser light is formed into a thin sheet (approximately 1 mm thick) using a cylindrical lens which excites 20-50 μm fluorescent, spherical poly(methyl methacrylate) (PMMA) Table 1 Experiment parameters and variables. X = gelatine concentration, H = gelatine layer depth, ρ = gelatine density, T mix = temperature of gelatine mixture when left to solidify, T = gelatine temperature when experiment commenced, t set = time cooling, Q = injection flux, E = Young's modulus, t = time to eruption, and Technique = experimental imaging and analysis technique applied (Pol = polarised light, Surf Def = surface elevation change monitoring, PIV = particle image velocimetry, DIC = digital image correlation).   Table 1, Fig. 1a and Supplementary Video Fig. S1).
passive tracer particles with a Rhodamine-B coating that gives peak fluorescence at a wavelength of 590 nm. The laser sheet is fired from the side of the tank and positioned vertically so it intersects with the injection point (Fig. 1b, c). The passive tracer particles are mixed into the injection fluid ( Fig. 1b) or the host gelatine during preparation of the experiment (Fig. 1c). Particles within the injecting fluid are added immediately prior to injection, and the fluid is kept in a container placed on a magnetic stirrer to ensure they remain in suspension during extraction. The particles are slightly denser than water and so over time they settle out of suspension, although this occurs over 10's of minutes and so is beyond the time of an individual experiment. The fluorescent particles are added to the hot gelatine mixture prior to it being left to cool, stirring it continuously before being placed in the refrigerator when it reaches 21°C . This ensures an even distribution of the tracer particles within the solidified gelatine.
Images are captured using a 2 MP CCD camera fitted with a 35 mm Nikon lens (Fig. 1b,c). The light reflected from the experiment is filtered using an optical longpass filter, which passes light with a long wavelength and blocks short wavelengths with a cut-in wavelength of 550 nm. This prevented the laser light that was reflected by the gelatine from entering the camera, thus allowing the light from the fluorescent particles to be clearly observed.
2.2.2.1. Calibration and pre-processing. Before each PIV or DIC experiment, an image is acquired of a 2D calibration target (an array of evenly-spaced black dots on a white background) aligned with the laser sheet and situated in the tank filled with water. Dantec Dynamic Studio imaging software detects the position and size of the filled-circles, and defines the area across which quantitative analysis can be accurately performed. This calibration image is later used in preprocessing to dewarp images of the experiment that are acquired. This process corrects for any distortion (which is minimal in our experiments and only occurs around the edges of the camera image; areas which are of little interest) as well as providing an accurate conversion between pixels and physical space. Great care is taken to ensure that the camera location, camera focus, tank location and laser sheet are not altered between this calibration step and the experiment itself.
2.2.2.2. Data processing and post-processing. After dewarping (described above) PIV cross-correlations produce vector fields (e.g. Adrian, 1991) using Dantec Dynamic Studio software. We utilise an adaptive correlation technique in which the interrogation windows have a 50% overlap. This results in a distance between vectors of 1.8 mm. Spurious vectors are removed using standard range and moving average validation techniques, and replaced with local mean values.
Post-processing of the vector fields is conducted in Matlab. As the region of interest increases in size throughout the experiment as the intrusion grows, we developed a masking technique that creates and applies a different mask for every PIV vector field. This is based on the region of interest being identified in the experimental images using an intensity threshold. This processing step eliminates vectors outside the region of interest that are purely the result of measurement noise.
For visualisation purposes only (figures and movies) a 3-by-3 spatial box is applied to the vector fields before plotting. In addition, it is evident that long time-averaging is not possible due to the constantly varying size of the intrusion. However, given that the timescale of the growth of the intrusion is significantly longer than the PIV capture rate we can average over a limited number of frames (10) such that each plot (or movie frame) is a short time-average (i.e. spanning 1.13 s in the PIV dyke flow experiments). Finally, to improve the clarity of the vectors in the visualisations, they are down-sampled by a factor of two (i.e. only every second vector is plotted) or three, depending on the type of experiment and visualisation. The colour-maps in all cases are not down-sampled and reflect the resolution of the experiments.
In the DIC experiments, strain is calculated from the post-processed vector field data. For the small strains in the sub-surface gelatine (significantly less than unity) the strain tensor can be linearised to give Cauchy's infinitesimal strain tensor: where v is the displacement vector, and x is the spatial coordinate. Thus, in the two-dimensions of interest in the DIC experiments, u and w are vector displacements in the x-and z-directions, respectively: and for the normal components of strain ϵ.
The shear components are equal due to symmetry, so: As the DIC provides discrete data on an even grid we simply estimate the gradients using a central differencing scheme, such that: ϵ zz ≈ w n;mþ1 −w n;m−1 2Δz ð12Þ and ϵ xz ≈ 1 2 where ϵ xx is the strain at the location (n, m). Note that Δx = Δz as the PIV interrogation windows are square (where Δx and Δz are the spacing between the vectors in the x and z directions, respectively). The error introduced by the discretisation of the equations is second order, Ο(Δx 2 ).

Results
The same experiment was carried out four times; each had the same gelatine concentration, volume and injection method, but a different imaging techniques was applied (see Table 1). Across the different techniques, we have identified four stages of dyke growth to eruption: 1) dyke inception, 2) dyke propagation, 3) pre-eruption ascent and 4) fissure eruption. The appearance of these different stages is now described in detail for each technique.

Dyke propagation geometry and sub-surface stress
A penny-shaped water-filled fracture was produced during injection. This experimental dyke propagated vertically (± 10°) towards the surface. Although qualitative, polarised light is very useful to  Table 1) up to the point of eruption, measured from the base of the injector. Stage 4 is not shown, but occurs at the end of the experiment as the dyke erupts. demonstrate the evolving stress field during dyke propagation using the photoelastic properties of gelatine. Coloured fringes depict stress contours, with high concentration of these indicating increasing stress intensity. The developing stress field and its distribution around the growing dyke is shown in Fig. 2 and Supplementary Video Fig. S1, showing stress is concentrated at the dyke tip and producing a 'bow-tie' of stress contours in the x-z plane ( Fig. 2i and ii). The visually-stressed region of gelatine is initially localised (Fig. 2ai,ii), but increases in extent as the dyke ascends (Figure 2bi,ii). Towards the surface, the stress field begins to intersect the surface and this continues to eruption (Fig. 2ci,ii).
Three stages of pre-eruption dyke growth can be identified based on the growing dyke geometry. Dyke length and width measurements based on HD video images are shown in Fig. 3a. In Stage 1 a circular geometry is developed (Fig. 2aiii), and this corresponds with approximately equal dyke length and width (Fig. 3a) although the rate of their growth decelerates over approximately the first 100 s of the experiment (Fig. 3b). In Stage 2, the dyke length and width continue to steadily grow at approximately constant velocity (Fig. 3b). Stage 3 marks the lead up to eruption, where the dyke begins to accelerate towards the surface, its length increases at a faster rate than its width, and it develops an elliptical geometry towards eruption (Fig. 2iii,c). At stage 4 the dyke tip reached the surface and it erupted to form a short fissure, and fluid was extruded onto the gelatine surface. The fissure measured approximately 5 cm in length, and the fissure margins were practically closed with an opening b0.1 mm through which fluid flowed. The data presented in Fig. 3 are from two identical experiments (Table 1), and they demonstrate the high degree of reproducibility between experiments.

Mapping fluid flow within a propagating and erupting dyke
In PIV experiments, passive tracer particles suspended in the injected fluid fluoresced in the y-z plane of the experimental dyke (see Supplementary Video Fig. S2a). Based on the fluid dynamics, the dyke propagation can be described in four stages (see Fig. 4 and Supplementary Video Fig. S2b): Stage 1: Fluid flow vectors within the first minute of experimental dyke growth were complex, but organised into two jets; one making a curved trajectory that is clockwise near the base of the injector, and the other moving in an anti-clockwise direction in the upper part of the dyke at the dyke margin (Fig. 4a). At this time the dyke was small (approximately 70 mm wide and 70 mm high), far from the gelatine surface (160 mm depth) and close to the injector, with a maximum flow velocity of 14.6 × 10 −3 m/s. Stage 2: After the initial dyke growth, the dyke fluid flow stabilises into one pseudo-steady, upward rising jet along the centre of the dyke (Fig. 4b). Flow velocities are maximum close to the injector, but the maximum flow speed has reduced to 6.6 × 10 − 3 m/s compared to stage 1. Flow vectors at the growing tip fan out and rotate to flow downwards at the dyke margin. The slowest flow velocities occur in two elliptical regions between the upward-flowing channel and the downflowing margin, where the fluid is almost static.
Stage 3: As the dyke approaches the surfaces to erupt, an instability develops in the flow. The central, upward jet meanders from side to side and at the base the fluid flow comprises two upward jets (Fig. 4c). The fastest moving fluid has migrated away from the injector and occupies a central band within the growing dyke, with slower velocities at the vertical tip and continued down-flow at the dyke margins. The maximum flow velocities in Stage 3 have slightly increased compared to stage 2 and are up to 6.9 × 10 −3 m/s. The two elliptical, almost-static, fluid regions between the upward jet and dyke margin remain and have grown in size.
Stage 4: The final stage of dyke ascent is the fissure eruption (Fig. 4d) when the flow dynamics within the dyke dramatically change. At the onset of eruption, all flow vectors are rapidly re-oriented upwards and towards the small fissure that formed in the gelatine surface. The upward jet from the injector and two jets at its base remain, though the region of static fluid rapidly increase in size from depth upwards. The fastest flow velocities of all dyke ascent stages are recorded, reaching 32.2 × 10 − 3 m/s as fluid is rapidly expelled and the dyke is drained.

Sub-surface incremental strain evolution during dyke ascent
In DIC experiments, passive-tracer particles within the gelatine solid were illuminated in the x-z plane presenting a cross-section around the growing experimental dyke (see Supplementary Video Fig. S3). The laser-illuminated plane reveals sharp margins of the dyke as it grows, and offers the opportunity to record in detail the evolving cross-sectional thickness variation as the dyke grows; in addition to quantifying the evolving incremental strain (ϵ xx , ϵ zz and ϵ xz ) using DIC. Based on the dyke thickness change and evolution in incremental strain, we identify four stages of dyke growth (Fig. 5): Stage 1: Sub-surface deformation of the gelatine during the early stages of dyke growth show the incremental strain is concentrated at the growing tip (Fig. 5a, 55 s). No incremental strain is recorded at the dyke tail region, indicating its opening is maintained. Vector arrows show the gelatine is displaced predominantly at the dyke margins, radiating from the growing tip, with larger lateral than vertical displacement. The largest component of incremental strain occurs in the horizontal direction (ϵ xx ); both vertical (ϵ zz ) and shear (ϵ xz ) components of strain are small. Overall incremental strain intensity in the early stages of dyke growth spans −2 -12 × 10 −3 ϵ xx , −2 -3 × 10 −3 ϵ zz, and −2 -3 × 10 −3 ϵ xz . Local positive ϵ xx occurs at the dyke tip and local negative ϵ xx occurs adjacent to the dyke tip, whereas local positive ϵ zz occurs just below the dyke tip and local negative ϵ zz just above this. Shear strain is also measured around the dyke tip.
Stage 2: As the dyke ascends, incremental strain continues to be concentrated at the growing tip and displacement arrows show continued outward radial movement at the dyke head with greater lateral than vertical displacement (Fig. 5b, 205 s). Similar patterns of ϵ xx , ϵ zz and ϵ xz occur compared to Stage 1, however their values have all slightly decreased. Uplift of the gelatine free surface is detected by a region of negative ϵ zz developing at the surface. Deflection of the dyke tip from vertical occurs as the dyke begins to propagate in an inclined plane, and this is when an asymmetrical pattern of incremental shear strain (ϵ xz ) is detected (lower negative ϵ xz occurs in the upper-right of the dyke tip relative to the lower-left). A small area of negative incremental strain ϵ xx occurs at the dyke tail region. The raw experimental image shows the tail of the dyke has pinched closed. In this stage of dyke propagation: ϵ xx ranges from −1 -7 × 10 −3 , ϵ zz ranges from −1 -2 × 10 −3 , and ϵ xz ranges from −1.5 -1.5 × 10 −3 .
Stage 3: Shortly prior to the dyke erupting, the dyke tip remains the focus of incremental strain; but, the magnitude and extent of the strain components significantly changes. The largest strain values are now in ϵ zz rather than ϵ xx . The intensity of negative vertical incremental strain (ϵ zz ) has increased in magnitude and extent. Asymmetry in negative ϵ xx is detected at the dyke tip, and asymmetry in ϵ xz remains. Small amount of incremental shear strain are detected at the gelatine's free surface. Overall in stage 3: ϵ xx ranges from − 1 -5 × 10 −3 , ϵ zz ranges from −6 -12 × 10 −3 , and ϵ xz ranges from −1 -1.5 × 10 −3 .
Stage 4: The moment immediately prior to dyke eruption is recorded as opening at the surface and the largest values of ϵ xx are then produced during the experiment. Displacement vectors are oriented towards the surface. Progressive 'zipping' closed of the tail occurs as displacement vectors rotate inwards at depth where small, localised regions of negative ϵ xx are produced. The largest incremental strain occurs in the horizontal component (ϵ xx ), followed by the shear strain ϵ xz (which is at its largest at stage 4) and then ϵ zz as the dyke completes its path to the surface. During this stage of dyke ascent ϵ xx ranges from −4 -14 × 10 −3 , ϵ zz ranges from −5 -3 × 10 −3 , and ϵ xz ranges from −5 -5 × 10 −3 . Fig. 6 shows the progressive deformation of the gelatine surface during an experiment as the dyke approached the surface. There was no change in surface topography detected during the majority of dyke ascent (see Supplementary Video Fig. S1c), and it was only when the dyke tip reached approximately b4 cm depth (during the final 120 s of ascent, see Fig. 6a) that an elevation change of the free-surface occurred. By the onset of fissure eruption, there was a gradual overall increase in elevation of 0.5 mm across the whole plane that was monitored. Local topographic highs (up to 1.5 mm) developed either side of the dyke tip (Fig. 6a). The elevation change was relatively broad early on, but became increased and focused as the dyke tip approached the surface. The dyke became slightly deflected from its vertical path (as is common in the experiments, e.g. Experiment 2, Fig. 5), as shown by an increase in the tip position relative to the injector (Fig. 6b). This slightly inclined propagation path resulted in the cumulative surface elevation change not being symmetrical, as the 'hanging wall' of the dyke developed a larger topography (up to 1.5 mm cumulative displacement) than the 'footwall' (approximately 0.9 mm of cumulative displacement).

Discussion: Coupled processes during dyke ascent and eruption
Most dykes in nature do not erupt (Gudmundsson, 2002) and the majority of magmas stall within the crust (Crisp, 1984). Determining if magma will breach the surface is of primary concern for volcanic hazard assessments. Dyke ascent in nature can be studied during ascent or post-emplacement; however, in both cases visualising the three-dimensional evolving geometry of the dyke is challenging and requires extrapolation from often two-dimensional datasets (Kavanagh, 2018). Evidence of magma flow, crust deformation and dyke eruption is only partially recorded. Our laboratory experiments can help inform the interpretation of natural data and challenge existing numerical models of dyke ascent.

Synthesising laboratory experimental results
The range of laboratory experiment monitoring techniques we have employed arguably represent the most detailed and comprehensive description and analysis of coupled fluid flow and host deformation during experimental dyke ascent to eruption. Dyke propagation involves the intrusion of a fluid into a solid, and our results emphasise the strong coupling between the intruding fluid and the deformation of its hostmaterial that influences magma ascent dynamics.
Four common stages of dyke ascent leading to eruption are evident in the experiments. 1) During dyke inception and its early growth, the fluid flow patterns are complex and comprise two circulating fluid jets. Strain is focused at the upper dyke tip as the penny-shape crack is progressively established. 2) As the dyke grows, the fluid flow within it stabilises into a single, rapid and upward flowing jet as the dyke grows in length and width at a constant and steady rate. 3) As the dyke approaches the surface our experiments show a fluid instability develops, causing the upward jet to meander and two jets to form at the dyke base. The origin of this instability is not clear, although its appearance corresponds with the time when the dyke tail pinches almostclosed, and when the dyke tip accelerates towards the surface. It is also at this stage that surface deformation is first recorded, resulting in the progressive increase in topography and elevation highs developing above the ascending dyke tip. 4) During dyke eruption, a small fissure is formed at the gelatine surface, a dramatic pressure release induces the rapid evacuation of fluid from the dyke, and the dyke walls 'zip' closed from the tail to the surface.

Challenging dyke ascent models
The patterns of surface elevation change we measured during dyke ascent agree well with that expected by analytical elastic models; the deformation comprised elevated regions either side of the dyke tip, with a relative low directly above it. Measurements of surface deformation at volcanic centres are often inverted for the source depth and source geometry using simple analytical models that assume intrusion into an isotropic, elastic host-rock. Our experimental observations therefore have the potential to be used to bench-mark these inverse models and inform their development.
The numerical models of dyke ascent that have been published can be divided into two end-member approaches (see Rivalta et al., 2015 for a review). Firstly, there are buoyancy-driven dyke ascent models that emphasise elasticity of the intruded media and its fracture toughness. In these models, the dyke becomes disconnected from its source (e.g. Weertman, 1971). Secondly, there are flux-driven dyke ascent models where the dyke is connected to its source and the fluid dynamics of the intrusion are described by applying lubrication theory (e.g. Lister, 1990aLister, , 1990band Spence et al., 1987). The circulation of fluid we observe in the experiments agrees well with the flow pattern expected by Dahm's (2000) dyke model, which emphasises the role of elasticity and fracture toughness but also reconciles the fluid dynamics of the intruding magma. However, this flow pattern contrasts with Roper and Lister (2007) who couple fluid flow and host deformation using lubrication theory and a dyke-scale process zone. Their model anticipates that, when connected to the source, dyke fluid flow should be predominantly vertical inside the dyke. However, our results suggest that, despite not having attained their 'buoyant length' and only having a small density contrast between intruding fluid and intruded host, our experimental dykes have the ascent dynamics expected of buoyant fluid-filled fractures in an elastic material, where the mechanical properties of the intruded host dominate the growth dynamics and the viscous resistance of the fluid to flow is minimal.
In our experiments, fluid is driven into the dyke at a constant volumetric flux and the dyke remains connected to its source. According to Linear Elastic Fracture Mechanics, the fluid-filled crack will propagate when the fluid overpressure exceeds the fracture pressure P f of the gelatine solid (Lister and Kerr, 1991): where K c is the fracture toughness of the gelatine and l is the crack length. Gelatine's K c can be estimated by the relationship (Kavanagh et al., 2013): In our experiments, E = 2000-3000 Pa and so we estimate K c = 63-77 Pa m 1/2 . However, the density difference between the injected fluid and the intruded gelatine also results in a buoyancy pressure P b (Rubin, 1995): where ρ s is the density of the solid (gelatine), ρ liq is the density of the liquid (water), g is gravity and L b is the buoyant length of the dyke (Eq. 2) (Taisne and Tait, 2009). Following these relationships, the calculated buoyant length of our experimental dykes is 1.3-1.4 m, where ρ s = 1002.5 kg/m 3 , ρ liq = 998 kg/m 3 and g = 9.81 m/s, which is much greater than the height of the experimental tank (0.3 m). It is therefore expected that the growth of our experimental dykes is flux-driven, and any buoyancy effects should be minimal.
The experimental dyke geometry in profile is circular in the early stages of dyke growth. This penny-shaped geometry is a consequence of intrusion into a homogeneous, isotropic elastic solid; in nature, however, anisotropy and mechanical heterogeneities of the crust are expected to influence the shape of the dyke (e.g. Kavanagh and Sparks, 2011). Fluid may also be fed into the dyke by a slit-like geometry rather than the nozzle-like injector we used. The dyke geometry evolved to become elongate as it approached the surface, in response to an accelerating dyke tip. In nature, mechanical heterogeneity of the crust will likely affect the dyke ascent rate and whether or not such an acceleration would occur. In cross-section, our experimental dyke developed a pinched tail and 'teardrop' morphology as the dyke propagated through the tank towards eruption. This geometry is similar to that expected of a 'Weertman crack', where a fixed volume injection ascends buoyantly though an elastic material (Weertman, 1971). This geometry occurred despite the crack receiving a constant flux of fluid, and remaining connected to the source (even if the connection is very small). Our experimental results therefore suggest the Weertman-crack geometry is not restricted to fixed volume injections, but can be developed by dykes that have sustained magma flux too. The analytical models that describe the buoyant length of fluid-filled fractures propagating in an elastic material therefore may not fully capture the dynamical processes of dyke ascent, and so will need to be revisited in the context of these new experimental observations.

Magma flow in nature
Our understanding of the dynamics of magma flow in dykes is limited to observations of volcanic fissure eruptions (e.g. Lundgren et al., 2013); in the early stages of eruption the magma exits along the fissure length, but rapidly the extrusion becomes focused at a few vents due to flow channelisation. The crystalline magma within ancient, solidified dykes offers the best access to the dyke; however, exposure is often limited to partial 2-dimensional sections and unravelling syn-and postemplacement textures from the time-sequence of magma solidification is difficult. However, there are several macroscopic flow indicators that can be used, including elongated vesicles that are aligned (e.g. Fig. 7), scour marks (e.g. Smith, 1987), phenocryst alignment (e.g. Bhattacharji and Smith, 1964), drag folds (e.g. Walker et al., 2017) and cataclastic elongation of phenocrysts (Smith, 1987). Magnetic fabrics, such as AMS have also been used to infer magma flow (e.g. Herrero-Bervera et al., 2001). Temporal variations in flow are postulated based on, for example, bubble-rich and bubble-poor coupled bands that suggest pressure fluctuations (see Fig. 7c and d). Any flow indicator needs to be used with caution, especially as the final stages of magma flow may be drainage or back-flow towards the source (e.g. Lundgren et al., 2013).
Our experimental results of the vectors of fluid flow during dyke intrusion and eruption provides important dynamical constraints that will likely aid the interpretation of flow fabrics within intrusions, in particular due to the identification of distinct stages of dyke ascent leading to eruption. In our experiments, the fluid initially circulated in two jets as the pre-cut was first filled and then the crack began to propagate. This early flow pattern was potentially an artefact of the initial injection conditions, and could have formed by the injector being partially blocked by incomplete breaking of the petroleum jelly seal. This first stage in the experimental dyke growth could vary between experiments, and so directly comparing this early stage of the experiment with natural observations is not recommended. However, after this initial stage the dyke width and length increased at constant velocity and this was when we observed a single jet to form and circulation of fluid within the propagating dyke. This jet persisted from these early stages of dyke growth up to immediately prior to eruption, with rapid evacuation of the dyke when it breached the surface. Our experimental observations therefore suggest that fluid flow trajectories within a nonfeeder dyke (that does not erupt) may be highly variable with upward, lateral and downward flow occurring. These would therefore be distinct from a feeder dyke where the flow velocity would be predominantly vertical, proffering the opportunity to assess whether or not a dyke erupted (even with limited exposure of the plumbing system) based on the flow vectors preserved but also depending on the timescale of solidification (e.g. Daniels et al., 2012). Jet formation and channelisation within natural dykes may occur in nature, resulting in progressive and preferred erosion of the country rock due to the sustained and rapid fluid flow, leading to the development of asymmetrical dyke geometries in the rock record (e.g. Kavanagh and Sparks, 2011). Variations in flow, either during intrusion or eruption, may lead to erosion of the mushy and progressively crystallising dyke margins. Our experimental dykes comprised a low viscosity Newtonian fluid, however during magma ascent it is likely that non-Newtonian fluid rheology such as shear-thinning will develop as the crystal and bubble-content of the magma increases. Future experiments will be required to assess the impact of non-Newtonian rheologies on the flow dynamics within a propagating dyke.

Host-rock deformation in nature
The conceptual framework used in our laboratory study is that dykes can be modelled as hydraulic fractures that intrude an elastic material, which is in-keeping with assumptions used during real-time monitoring and inversion modelling of intrusion-induced deformation at active volcanoes. However, an important consideration in dyke ascent mechanics is understanding under what circumstances they create their own fractures or instead intrude pre-existing weak planes. This is important for hazard assessment and predicting the sites of future vents from dyke ascent e.g. in a monogenetic volcanic field (e.g. Le Corvec et al., 2013b). The sub-surface deformation patterns we observe in our experiments, such as incremental strain and stress field evolution, could be helpful to interpret seismicity during active intrusion. The surface deformation patterns could be helpful to inform the interpretation of tilt meter data, GPS monitoring networks and InSAR analysis.
Field evidence of host deformation associated with dyke ascent ranges from macro-to micro-scale. Dyke-parallel fractures at the dyke margins within sedimentary (Delaney et al., 1986) or igneous hostrocks (Brown et al., 2007;Kavanagh and Sparks, 2011) may suggest these were pre-existing structures that were exploited by the ascending magma, although the exploitation of existing fractures is likely to be a relatively near-surface process (Rubin, 1995). A potentially valuable, yet unexplored, tool to study the micro-scale damage zone surrounding hydraulic fractures (e.g. dykes) are Fluid Inclusion Planes (FIPs). FIPs appear under optical microscopy as small linear "bubble" trails in individual crystals and are thought to be fossilised microfractures which are the result of healing, or "necking down" of previously open fractures which functioned as fluid pathways (Roedder, 1984). FIPs can provide valuable information when studying rock deformation as they can provide insight into deformation geometries, chronology of deformation (Lespinasse, 1999;Pecher et al., 1985) and are potential indicators to the paleostress field (Lespinasse and Pecher, 1986). The healing process is relatively quick in relation to geological time (Smith and Evans, 1984) and they form as Mode I fractures, occur predominately perpendicular to the least principal compressive stress axis, σ 3 , with no evidence of shear displacement which would be expected from Mode II/III fractures (Lespinasse, 1999). Quartz is a common mineral for FIPs to be observed as, due to its crystallographic properties, fractures in quartz are usually formed in response to the regional stress field (Lespinasse and Cathelineau, 1990). Minerals such as feldspars, however, which have more complex cryptographic features, such as twinning and the presence of cleavages, can alter the preservation or have preferred orientations of FIPs (Lespinasse, 1999). Observations of FIPs can be made optically at magnifications as low as ×10, as shown in Fig. 8a; however optical observations are somewhat hindered due to the healing process, making many FIPs invisible in plane polarised and cross polarised light. The use of a Scanning Electron Microscope fitted with a Cathodoluminescent detector (SEM-CL) can dramatically increase the number of observable FIPs by up to 100% in some cases. This is demonstrated in the optical micrograph Fig. 8a, which shows roughly 8 visible FIPs, compared to the SEM-CL micrograph Fig. 8b, which has 16 potential FIPs. The SEM-CL provides a more complete image of FIPs, making it a more effective structural tool to assess host-rock damage around dykes.

Conclusions
The laboratory methods we have employed have allowed the detailed description and quantification of coupled fluid flow and host deformation during the inception, growth and eruption of an experimental dyke. We have identified four phases of dyke ascent: Stage 1: Dyke inception and early growth. Fluid flow is complex, circulating as the dyke grows equally in breadth and length creating a penny-shaped geometry. Sub-surface deformation is focused at the growing tip, with material at the dyke tip margin progressively displaced outwards, and stress concentration showing a 'bow-tie' geometry. No surface elevation change is recorded as the dyke is formed and begins to grow.
Stage 2: Dyke propagation. Fluid flow comprises a rapid, centralised, upward-rising, pseudo-steady jet with slow down-welling at the dyke margin. Regions of static fluid develop within the circulating flow. Sub-surface deformation remains concentrated at the growing tip, shown by a concentration in incremental strain and stress. The dyke tail pinches almost-closed at depth at the end of this stage.
Stage 3: Near-surface ascent. A flow instability develops as the upward and centralised rapid fluid flow begins to meander and move from side to side. Two jets at the base of the dyke feed into the upper single jet, and slower fluid continues to down-well at the growing dyke margin. The dyke begins to lengthen, developing an elliptical geometry as the dyke tip begins to accelerate towards the surface. The pinched tail of the ascending dyke migrates towards the surface. The dyke trajectory is deflected as shear stresses intensify, and the dyke stress field begins to interact with the surface. The inclined dyke produces an asymmetrical cumulative elevation change centred above the dyke.
Stage 4: Fissure eruption. Rapid opening of the dyke occurs as it intersects the surface and produces a short fissure. This depressurisation causes rapid evacuation of fluid from the dyke. Flow is focused towards the vent and the active-region of flow is increasingly focused towards the surface as the pinched dyke tail zips closed from depth and accelerates towards the surface.
The experimental results emphasise the importance of considering coupled fluid flow and host deformation when developing the next generation of dyke ascent models, to inform the interpretation of the field and geophysical evidence of ancient, ongoing, and future dyke intrusion events.